Here \(M_P\)  represents planck's mass and \(D=4\)  i.e. for \(4-D\)  spacetime. The planck's mass is used in correspondence to express to the gravitational coupling strength. In the realm of higher dimensional spacetime i.e. \(D>4\) , [1]} performing quadratic curvature corrections to the Einstein Hilbert action leads to the Einstein\(-\) Gauss\(-\)  Bonnet (EGB) theory. Lovelock's Theorems [2]}, [3]} into higher dimensions are fundamentally generalisation of Einstein's Equation in higher dimensions. The main advantage in Lovelock's theorem is the equations of motions are second order variants of the metric which makes it much more mathematically lucid with respect to the other gravity theories that are 4th or higher derivatives of the metric. It is an intriguing matter that the [4]} Einstein Gauss Bonnet gravity can be classified as a special case of Lovelock's theorem, as the quadratic curvature corrections obtained in this method is through variation of the Gauss - Bonnet term. Zwiebach [5]} provided us that Gauss-Bonnet term is the lone pertinent method to perform higher derivative combination for the leading correction to Einstein theory, in the low energy effective string theory. The EGB theory basically amalgamates a single term to Einstein-Hilbert action which is quadratic in Riemann tensor which naturally serves as the action of Low energy heterotic string theory [6]}, [7]}, [8]} . The low energy effective string theory is quite a promising theory as it appears to be a prominent theory of gravity in higher dimension as it complies higher order curvature terms in the action. This theory is considered be a contender to remove the singularity problem in Einstein's general relativity.
